Question

square measure conversions

\\(144\text{ in.}^2 = 1\text{ ft.}^2\\)

\\(9\text{ ft.}^2 = 1\text{ yd.}^2\\)

\\(4,840\text{ yd.}^2 = 1\text{ acre}\\)

\\(43,560\text{ ft.}^2 = 1\text{ acre}\\)

\\(640\text{ acres} = 1\text{ mi.}^2\\)

drag and drop the correct option to complete the sentences.

if a developer charges \\(p\\) dollars per square footage, the total price of a plot with \\(a\\) acres can be given by the formula \\(\text{total price} = p \cdot a \cdot \text{ }\\).

here \\(p\\) has the units \\( \\).

Explanation:

Identify the conversion factor

The problem states that a developer charges \(p\) dollars per square footage (which means dollars per square foot, or \(\text{dollars}/\text{ft}^2\)).
We need to find the total price of a plot with \(a\) acres.
From the given table of "Square Measure Conversions", we have:

$$1\text{ acre} = 43,560\text{ ft}^2$$

Set up the formula

To find the total price, we multiply the rate by the total area in square feet:

$$\text{Total Price} = \text{Rate} \times \text{Area in square feet}$$

Since the area is given as \(a\) acres, we convert acres to square feet:

$$\text{Area in square feet} = a\text{ acres} \times 43,560\text{ ft}^2/\text{acre} = 43,560 \cdot a\text{ ft}^2$$

Now, multiplying by the rate \(p\) (in dollars per square foot):

$$\text{Total Price} = p \cdot (43,560 \cdot a) = p \cdot a \cdot 43,560$$

Thus, the missing value in the formula \(\text{Total Price} = p \cdot a \cdot \text{[blank]}\) is \(43,560\).

Determine the units of p

The rate \(p\) is defined as "dollars per square footage".
"Square footage" is measured in square feet (\(\text{ft}^2\)).
Therefore, the units of \(p\) are dollars per square foot, which can be written as \(\text{dollars}/\text{ft}^2\).

Answer:

If a developer charges \(p\) dollars per square footage, the total price of a plot with \(a\) acres can be given by the formula \(\text{Total Price} = p \cdot a \cdot\) <blank>\(43,560\)</blank>.

Here \(p\) has the units <blank>\(\text{dollars}/\text{ft}^2\)</blank>.